GLOBAL BOUNDEDNESS OF SOLUTIONS TO A CHEMOTAXIS-FLUID SYSTEM WITH SINGULAR SENSITIVITY AND LOGISTIC SOURCE

被引：25

作者：

Ren, Guoqiang ^{[1
,2
,3
]}

Liu, Bin ^{[1
,2
]}

机构：

[1] Huazhong Univ Sci & Technol, Sch Math & Stat, Wuhan 430074, Peoples R China

[2] Huazhong Univ Sci & Technol, Hubei Key Lab Engn Modeling & Sci Comp, Wuhan 430074, Peoples R China

[3] Huazhong Univ Sci & Technol, Inst Artificial Intelligence, Wuhan 430074, Peoples R China

来源：

COMMUNICATIONS ON PURE AND APPLIED ANALYSIS | 2020年 / 19卷 / 07期

关键词：

Chemotaxis-fluid; logistic source; global bounded; singular sensitivity; asymptotic behavior; NAVIER-STOKES SYSTEM; TENSOR-VALUED SENSITIVITY; SMALL-CONVECTION LIMIT; KELLER-SEGEL SYSTEM; WEAK SOLUTIONS; GENERALIZED SOLUTIONS; NONLINEAR DIFFUSION; ASYMPTOTIC-BEHAVIOR; EXISTENCE; STABILIZATION;

D O I：

10.3934/cpaa.2020170

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we investigate the chemotaxis-fluid system with singular sensitivity and logistic source in bounded convex domain with smooth boundary. We present the global existence of very weak solutions under appropriate regularity assumptions on the initial data. Then, we show that system possesses a global bounded classical solution. Finally, we present a unique globally bounded classical solution for a fluid-free system. In addition, the asymptotic behavior of the solutions is studied, and our results generalize and improve some well-known results in the literature, and partially results are new.

引用

页码：3843 / 3883

页数：41

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